The “memristor” concept was introduced in 1971 by L. O. Chua in the article “Memristor—The Missing Circuit Element”, IEEE Transactions on Circuit Theory, Vol. CT-18, 1971, pages 507-519.
Theoretically, a memristor is defined as an element (more exactly, an electrical dipole) in which the magnetic flux ΦB depends on the electric charge q that has passed through the element. The “memristance” M(q) is defined by:
      M    ⁡          (      q      )        =            ⅆ              Φ        B                    ⅆ      q      
It is possible to demonstrate that it follows from this definition that:V(t)=M(q(t))I(t)
where V(t) is the voltage across the terminals of the dipole and I(t) the current flowing through it, both expressed as a function of time t. In other words, at any moment M(q) is equivalent to a resistance the value of which varies as a function of q, and therefore of the “history” of the current I (the trivial case where M(q)=R, i.e. a constant, and the memristor could be replaced by an ordinary resistor is not considered here).
If the V-I characteristics of a memristor are plotted, in general a curve exhibiting a double hysteresis cycle is obtained, as illustrated in FIG. 1.
Because of this characteristic, certain memristors exhibit a bistable behavior and can be used as nonvolatile memory elements. Applying a voltage across the terminals of such a device causes a large variation in its resistance; for example, it passes from a high value, representing a logic value of “1”, to a low value, representing a value of “0”. As the V-I characteristics exhibit hysteresis, this resistance value is maintained when the voltage drops to zero; it is necessary to apply an inverse voltage in order to return to the initial (high) resistance value.
This bistable behavior also allows matrices of memristors to be used to carry out logic operations. See in this regard the article by J. Borghetti et al. “‘Memristive’ switches enable ‘stateful’ logic operations via material implication”, Nature, Vol. 464, pages 873-876, 8 Apr. 2010.
Even before the “memristor” concept had been formulated, certain materials, and especially thin films of TiO2, were already known by the electrochemists community, from the 1960s, to exhibit a behavior that could be qualified as “memristive”: see the article by F. Abgall “Switching phenomena in titanium oxide thin films”, Solid-State Electronics 1968. Vol. 11, pages 535-541.
Production of an electronic element that could be qualified as a “memristor” was described for the first time in the article by D. B. Strukov et al. “The missing memristor found”, Nature, Vol. 453, pages 80-83, 1st May 2008. This element used a TiO2/TiO2-x bilayer as an active material. See also documents US 2008/0079029, U.S. Pat. No. 7,763,880 and U.S. Pat. No. 7,417,271, which also envisage a possible generalization to other oxides, optionally of relatively complex composition.
The resistivity change that is the basis of the memristive behavior of these prior-art elements is caused by the migration, induced by an electric field, of dopant species—and in particular of oxygen vacancies—from a first conductive film that is rich therein to a second film that is deprived thereof, and that is therefore less conductive. The drawback of these devices is the relative complexity of the manufacture of the bilayer (even, in certain cases, the multilayer) structure.
As for the device described in the aforementioned article by J. Borghetti et al., it comprises just one TiO2 film sandwiched between two metallic films. It is known, in such a structure, that the dopant species (oxygen vacancies) form conductive filaments between the two metallic electrodes; see in this regard the articles by R. Waser “Nanoionics-based resistive switching memories”, Nature materials, Vol. 6, pages 833-840, November 2007, and “Redox-Based Resistive Switching Memories—Nanoionic Mechanisms, Prospects and Challenges”, Advanced Materials 21, pages 2632-2663, 2009. The growth of these conductive filaments is a random process that takes place along lattice dislocations. It is therefore difficult to ensure the presence of at least one of these filaments in a nanoscale device, thereby preventing its reliable operation. Therefore, a resistance-switching mechanism based on the formation of filamentary conductive pathways is intrinsically of a nature to limit device miniaturization.
It should also be underlined that the initial formation of these conductive filaments requires a preliminary film “electroforming” step, which is still little understood and therefore difficult to control (J. J. Yang et al., Nanotechnol., 2009, 20, 215201).
Document WO 2010/074689 reports memristive devices comprising a single active region, produced from a material comprising at least two mobile species. Several families of materials of this type are mentioned, among which substitution compounds in which alkali-metal atoms replace transition-metal atoms in order to form interstitial defects that act as dopants. It would seem that an electroforming step is also necessary to ensure that these devices operate (see the aforementioned article by J. Yang et al.).
Document US 2010/102289 describes a resistive memory element the active region of which comprises two films that are metallic or made of metal oxide, one of which is doped with a charge carrying species, these two films being separated by an intermediate film produced from a material other than that or those of the two other films. Production of such a device is complex.
Document WO 2008/145864 describes the use of insertion compounds of at least one alkali metal, made of an oxide or chalcogenide of at least one transition metal, exhibiting conductivity that is both electronic and ionic in nature and, most often, having a lamellar structure, to produce mass memories. Certain of these materials, such as NaxCoO2 and LixCoO2 (0<x≦1), are known as materials used to produce electrochemical batteries. See document EP 1 860 713, for example.
The mass memories described in the aforementioned document WO 2008/145864 comprise a bulk single-crystal substrate made of such a material, above which an atomic force microscope (AFM) probe is placed. A water meniscus forms spontaneously between the probe and the surface of the substrate; this meniscus ensures electrical conduction between these two elements and forms an electrochemical cell in which redox reactions can take place. It is precisely electrochemical reactions of this type, induced by applying a potential difference between the AFM probe and the substrate, that form the basis of operation of the mass memory.
Specifically, a change in the oxidation number of a transition-metal atom is accompanied by an inserted (or “intercalated”, the two terms being equivalent) alkali-metal atom being ejected to the surface, or, conversely, being returned to the core of the substrate, producing a reversible change in surface conductivity. See in this regard the following articles:    O. Schneegans, A. Moradpour, O. Dragos, S. Franger, N. Dragoe, L. Pinsard-Gaudart, P. Chretien, A. Revcolevschi, J. Amer. Chem. Soc, 2007, 129, 7482; and    O. Schneegans, A. Moradpour, L. Boyer, D. Ballutaud, J. Phys. Chem. B, 2004, 108, 9882.
Such memories are very difficult and expensive to implement: the single-crystal substrates are difficult to manufacture and some of them, such as NaxCoO2, are unstable in air; the use of AFM probes introduces considerable complexity and requires a movable read head to scan the surface of the substrate.